Observer-Based Leader-Following Consensus of General Linear Multiagent Systems Based on Novel Event Trigger Mechanism with Input Time Delay under Directed Graphs

Hong Zhang,Feng Wei,Changshun Chen,Xiao Ling Wang

doi:10.1155/2021/4760249

Abstract

This paper considers the tracking and containment consensus for the general linear systems with input time delays under directed communication networks. The distributed observer-based algorithm on the basis of event-triggering mechanism will be designed by using only neighboring agents information. In this way, we can save network resource effectively. The event-based protocol with input time delays will be proposed for the leader-follower systems. Appropriate feedback gain matrices and trigger parameters can be designed by using Lyapunov stability theory. Based on the designed control algorithm, if the feedback gain matrices and the event trigger are designed appropriately, the leader-follower general linear system can eventually reach tracking and containment consensus. Then, two simulation results are provided to demonstrate the practicability of the theoretical analysis.

Highlights

In recent years, the multiagent systems have been paid considerable attentions in various scientific communities, such as spacecraft formation flying, complex network control, and collaborative monitoring [1, 2]
For the consensus issues of multiagent systems, the main work is to design a suitable information exchange method so that all agents can agree on the state of interest. e research studies on multiagent systems’ consensus issues mainly focus on communication topology, agent dynamic systems, and control method, which emphasize the specific analysis of the whole system
E earlier related research studies mainly focus on the leaderless consensus issues, which means the final state of the agents will be not set in advance

Summary

Introduction

The multiagent systems have been paid considerable attentions in various scientific communities, such as spacecraft formation flying, complex network control, and collaborative monitoring [1, 2]. In [14], the authors study the distributed containment control issues and design the corresponding control algorithm for the general linear system which can make the leader-follower system reach containment consensus. E distributed observer-based tracking and containment control algorithms by using the event-triggered control method are, respectively, proposed for general linear systems with time delays in [33, 34]. We will consider the tracking and containment consensus issues for the leader-follower general linear systems with time delays under directed graph. Two fully distributed observer-based control protocols by using the event-triggered method are proposed for both tracking control and containment control problems of the leader-follower linear systems with time delays. A ⊗ B denotes the Kronecker product of matrices A and B. λm means the maximum eigenvalue of a real matrix. conv􏼈x1, x2, . . . , xN􏼉 􏽮􏽐Ni 1 αixi|αi ∈ R, αi ≥ 0, 􏽐Ni 1 αi 1􏽯 represents the convex hull of the set x1, x2, . . . , xN. dis{x, U} infy∈U‖x − y‖ represents the Euclidean distance between the point x ∈ R and the set U⊆R

Preliminaries and Problem Formulation

Main Result

Simulation Example